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Theorem socnv 31630
Description: The converse of a strict ordering is still a strict ordering. (Contributed by Scott Fenton, 13-Jun-2018.)
Assertion
Ref Expression
socnv (𝑅 Or 𝐴𝑅 Or 𝐴)

Proof of Theorem socnv
StepHypRef Expression
1 cnvso 5662 . 2 (𝑅 Or 𝐴𝑅 Or 𝐴)
21biimpi 206 1 (𝑅 Or 𝐴𝑅 Or 𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4   Or wor 5024  ccnv 5103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-9 1997  ax-10 2017  ax-11 2032  ax-12 2045  ax-13 2244  ax-ext 2600  ax-sep 4772  ax-nul 4780  ax-pr 4897
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3or 1037  df-3an 1038  df-tru 1484  df-ex 1703  df-nf 1708  df-sb 1879  df-eu 2472  df-mo 2473  df-clab 2607  df-cleq 2613  df-clel 2616  df-nfc 2751  df-ne 2792  df-ral 2914  df-rab 2918  df-v 3197  df-dif 3570  df-un 3572  df-in 3574  df-ss 3581  df-nul 3908  df-if 4078  df-sn 4169  df-pr 4171  df-op 4175  df-br 4645  df-opab 4704  df-po 5025  df-so 5026  df-cnv 5112
This theorem is referenced by:  wzelOLD  31746
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